scholarly journals Asymptotic behaviour for local and nonlocal evolution equations on metric graphs with some edges of infinite length

2020 ◽  
Author(s):  
Liviu I. Ignat ◽  
Julio D. Rossi ◽  
Angel San Antolin
Keyword(s):  
Asymptotic Behaviour ◽  
Evolution Equations ◽  
Infinite Length ◽  
Metric Graphs ◽  
Nonlocal Evolution Equations

scholarly journals Normal Hyperbolicity and Continuity of Global Attractors for a Nonlocal Evolution Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Severino Horácio da Silva ◽  
Jocirei Dias Ferreira ◽  
Flank David Morais Bezerra
Keyword(s):  
Evolution Equation ◽  
Lower Semicontinuity ◽  
Evolution Equations ◽  
Upper Semicontinuity ◽  
Global Attractors ◽  
Functional Parameter ◽  
Normal Hyperbolicity ◽  
Nonlocal Evolution Equations

We show the normal hyperbolicity property for the equilibria of the evolution equation∂m(r,t)/∂t=-m(r,t)+g(βJ*m(r,t)+βh),  h,β≥0,and using the normal hyperbolicity property we prove the continuity (upper semicontinuity and lower semicontinuity) of the global attractors of the flow generated by this equation, with respect to functional parameterJ.

scholarly journals A Compactness Tool for the Analysis of Nonlocal Evolution Equations

2015 ◽  
Vol 47 (2) ◽  
pp. 1330-1354 ◽  
Author(s):  
Liviu I. Ignat ◽  
Tatiana I. Ignat ◽  
Denisa Stancu-Dumitru
Keyword(s):  
Evolution Equations ◽  
Nonlocal Evolution Equations
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